One common assumption to cope with confounding bias is that to assume no unobserved confounders exist [1]}, or more generally, the ignorable treatment assignment assumption [2]}, which states that the treatment assignment is independent of the potential outcomes caused by the treatment, given the background data available. Although a number of methods are proposed based on this assumption [3]}, [4]}, [5]}, it can be too restrictive, since it is often difficult to determine how the confounder affects treatment assignments and outcomes.
